Periodic solutions for the p-Laplacian neutral functional differential system

Zhenyou Wang,Changxiu Song

doi:10.1186/1687-1847-2013-367

Abstract

By using the generalized Borsuk theorem in coincidence degree theory, we prove the existence of periodic solutions for the p-Laplacian neutral functional differential system.

Highlights

In recent years, the existence of periodic solutions for the Rayleigh equation and the Liénard equation has been studied
Motivated by the works in [ – ], we consider the existence of periodic solutions of the following system: d d dt φp x(t) – Cx(t – τ )
By using the theory of coincidence degree, we obtain some results to guarantee the existence of periodic solutions

Summary

Introduction

The existence of periodic solutions for the Rayleigh equation and the Liénard equation has been studied (see [ – ]). Motivated by the works in [ – ], we consider the existence of periodic solutions of the following system: d d dt φp x(t) – Cx(t – τ ) + grad F x(t) + grad G x(t) = e(t), dt where F ∈ C (Rn, R), G ∈ C (Rn, R), e ∈ C(R, Rn) are periodic functions with period T ; C = [cij]n×n is an n × n symmetric matrix of constants, τ ∈ R is a constant.

Results

Conclusion